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Flipping two coins, F is at most one tail and G is two faces the same. Are F and G mutually exclusive?
ANo, because they share the outcome HH
BYes, because they share no outcome at all
CNo, because they share the outcome TT
DYes, because their probabilities differ
Answer & Solution
Correct answer: A. No, because they share the outcome HH
1. Event F, at most one tail, holds HH, TH and HT.
2. Event G, two faces the same, holds HH and TT.
3. Both events contain HH, so their joint probability is not zero.
4. Sharing even one outcome is enough to rule out mutual exclusivity, whatever the two probabilities are.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.2 Independent and Mutually Exclusive Events_
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